Bending of Reissner’s plate containing a through-the-thickness crack by concentrated moments taking into account the width of a contact zone of its faces

Abstract

We investigate the stress-strain state of an infinite isotropic plate with a crack the faces of which are free of external loading. The plate is under the action of concentrated bending moments. It is assumed that the crack faces are in a smooth contact along the entire length of the crack in the two-dimensional zone of constant width near the upper base of the plate. As a result of the contact of the crack faces, a solution of the problem is presented in the form of solutions of two related problems: a plane problem of the theory of elasticity and a problem of bending of plates using the Reissner theory. Using methods of the theory of functions of complex variable and complex potentials, we obtain a system of singular integral equations and numerically solved this system by the method of mechanical quadratures. In the case of geometric and physical symmetry of the problem with respect to the crack, we perform the numerical analysis of a solution of the problem and plot graphic dependences of the contact force between the faces of the crack and moment intensity factors for different parameters of the problem.